Problem: Solve for $x$ and $y$ using elimination. ${6x+y = 43}$ ${5x+y = 37}$
Explanation: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the top equation by $-1$ ${-6x-y = -43}$ $5x+y = 37$ Add the top and bottom equations together. $-x = -6$ $\dfrac{-x}{{-1}} = \dfrac{-6}{{-1}}$ ${x = 6}$ Now that you know ${x = 6}$ , plug it back into $\thinspace {6x+y = 43}\thinspace$ to find $y$ ${6}{(6)}{ + y = 43}$ $36+y = 43$ $36{-36} + y = 43{-36}$ ${y = 7}$ You can also plug ${x = 6}$ into $\thinspace {5x+y = 37}\thinspace$ and get the same answer for $y$ : ${5}{(6)}{ + y = 37}$ ${y = 7}$